I don’t know about the efficiency of a gas furnace, but I do know of two separate family members who got CO2 poisoning because of faulty furnaces. Both suffered severe brain damage as a result.
My daughter has a gas furnace vented directly into her chimney. There is only about two feet distance between them. To vent hers through a wall would require about fifteen feet of horizontal run and I would not trust it.
I have vent free heaters in my bedrooms and keep a window open slightly to provide air.
In my den I installed a ventless fireplace and I immediately began to have problems with fumes in the den. After a couple of years, I pulled out the burner and found that the air inlet to the mixing chamber was only two drilled 1/4 inch holes. I then drilled a third hole and have had no problems since.
What makes me wonder about the fireplace is that I purchased it FROM MY GAS COMPANY! They should have known better!
Why wouldn’t you trust a horizontal vent pipe? You have to support it every four feet and if it sags you will get condensate buildup in the pipe and your pressure switch will shut the gas valve off. The safeties on furnaces these days prevent lots of problems from getting out of hand.
Me, I never worry about CO2 either. My windows are so old and breezy, I couldn’t die of monoxide poisoning if I tried with a gas grill!
No money = no new windows. Oh Well!
On a more serious note, if you have an older gas furnace, I don’t care which brand (***ox comes to mind)every other year of so, pay your service man to DYE CHECK the manifold. Its a simple procedure, and is extremely accurate in detecting cracks in the unit. Manifold cracks are killers. Literally.